A highly simplified one-dimensional model of protein folding has been developed in which the driving force is the attempt to achieve uniform internal density. The polypeptide chain is described as point-like beads on a polynomial curve, and the local density of beads is represented using wavefunctions. Despite the physical and mathematical simplicity of the model, it nonetheless displays chaotic behaviour, and analogies can be drawn to the molten-globular state, the transition state and the correctly folded state. The results support a more random view of protein folding than is often seen in the literature.